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The fourth seed swept past Slovenia's Tamara Zidansek 6-2, 6-4 to set up an all-Asian clash with Hsieh Su-wei of Taiwan in the next round.
Osaka, who won her maiden Grand Slam at the US Open last year, struggled to close out the match after a strong start but always looked in control against the world number 78.
"I thought I served alright, this was my first time playing her and I'm just happy to win to be honest," the 21-year-old said.
"I know I could have made less unforced errors (23) this match. So that's the biggest thing I take away."
The softly-spoken 21-year-old's profile has soared since her victory at Flushing Meadows, particularly since it was done in the face of Serena William's infamous rant at the umpire in the decider.
She was bashful when told that fellow 21-year-old Zidansek had felt intimidated before facing her on Margaret Court Arena.
"No way! I feel old," she said. "Wow, that's kind of crazy... It's weird.
"For me, when I play, like, Venus (Williams) or someone, I'm star struck too . It's a bit weird when you tell me there's someone I'm playing that feels that way."
She anticipated a tough test against Hsieh, who she defeated in their only previous meeting.
"She's been playing really well recently so I just hope that it's exciting," she said.
"I feel like playing her is going to be really hard because she slices a lot. That's something I'm not used to that much, so I'll have a practice a lot tomorrow."
Osaka was in no mood to hang around after rain delayed the start of play against Zidansek as the show court roof was closed.
She broke Zidansek in the first game, only to allow the Slovenian to get back on level terms in the fourth with a string of unforced errors.
It proved a minor wobble, with Osaka restoring her advantage with a lob that left Zidansek flat footed, then claiming another break before serving out the set in 28 minutes.
The second set was tighter as Osaka uncharacteristically struggled on serve, double faulting as Zidansek went up a break.
But she made amends in the next game and saw off two break points from Zidansek before bringing up two match points on serve.
Osaka netted a forehand return on the first one but Zidansek could not handle the power of her second, hitting it into the crowd to hand the Japanese player victory.
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